Problem: Divide. Write your answer in simplest form. $ -\dfrac{5}{4} \div \dfrac{4}{3} = {?} $
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{4}{3}$ is $\dfrac{3}{4}$. Therefore: $ -\dfrac{5}{4} \div \dfrac{4}{3} = -\dfrac{5}{4} \times \dfrac{3}{4} $ $ \phantom{-\dfrac{5}{4} \div \dfrac{4}{3}} = \dfrac{-5 \times 3}{4 \times 4} $ $ \phantom{-\dfrac{5}{4} \div \dfrac{4}{3}} = -\dfrac{15}{16} $